{"paper":{"title":"The two-disjoint-copies property for compact spaces, homogeneity and connection with $C_p$-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Jerzy K\\k{a}kol, Ond\\v{r}ej Kurka, Wies{\\l}aw \\'Sliwa","submitted_at":"2026-06-25T21:52:38Z","abstract_excerpt":"A Tychonoff space $X$ has the two-disjoint-copies property (2DCP) if there exists a sequence $(K_n)_{n\\in\\omega}$ of non-empty compact subsets of $X$ such that each $K_n$ contains two disjoint subsets homeomorphic to $K_{n+1}$. Banakh, K\\k{a}kol and \\'Sliwa showed that 2DCP yields an infinite-dimensional metrizable quotient of $C_p(X)$, while it is still a long-standing open question whether $C_p(X)$ has such a quotient for any infinite compact space $X$. The above concept as well as the last problem are closely related to Efimov's problem that has remained open for 40 years. We will discuss a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27568","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.27568/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}